Over LAN. The thing about my home garage is that it's at my home where my wifi is. NAT and ipv6 doesn't enter the discussion if I'm already on my home wifi.
It does not seem unreasonable that a users might want to open the door while they are coming down the street or turning into the driveway, before they are within wifi range. Maybe their home wifi just barely reaches the inside of the garage and doesn't extend past the garage door. Most folks are not exactly wireless network experts.
I agree it would be ideal to use a local network path if possible, but given that remote access is a requirement, I can understand why they just made it the default.